How to get current page URL from backing bean?

You can get a reference to the HTTP request object via FacesContext like this:

FacesContext fc = FacesContext.getCurrentInstance();
HttpServletRequest request = (HttpServletRequest) fc.getExternalContext().getRequest();
}}

and then use the normal request methods to obtain path information. Alternatively, 
{{{context.getViewRoot().getViewId();

will return you the name of the current JSP (JSF view IDs are basically just JSP path names).